Today we will talk a little bit about how the catalog of functions will actually work. A more formal and comprehensive description of this is the function model, but here we want to create a more intuitive explanation.

Every page in the new wiki will contain one Object. Every Object is of exactly one Type. Types decide what the Object means. Types also decide what makes an Object valid or not. An Object that is of a certain Type is called an instance of that Type. Every Object that is stored as a wiki page is called a Persistent Object, and such an Object has a Z-ID by which it can be referenced. The Z-ID is the name of the page.

What does it mean that the Type decides what the Object means? Let’s look at an example. An Object of Type Positive Integer with the value "2020" represents the number 2020. That’s the number you get when you multiply 4, 5 and 101. And because it has the Type of Positive Integer, we know it is a number. If the Type of "2020" was String, then that wouldn’t represent the number 2020, but rather a sequence of four characters, "2", "0", "2", and 0. If the Type of it was Gregorian Calendar Year then this would represent the year 2020 in that calendar, a leap year starting with a Wednesday and ending with a Thursday.

The Type decides what you can do with an Object -- or, more formally speaking, which Functions you can apply to the given Object. If you have a String, you can count the length of the String, i.e. how many characters are in the sequence. The result for "2020" above would be four. If you have a Gregorian Calendar Year, you might also be able to ask for the 'length', but the result should probably be 366 days (as it is a leap year). If you have a Positive Integer and ask for its length, you might be asking for the logarithm in base 10, or you might be asking for the multiplicative persistence. But all of these would be different Functions (that may well have the same label, “length”, in English; their descriptions would explain in more detail what they would do). The Function states which Types it can take, and the Type decides what an Object means.

Types can be very diverse. Some Types might have a small, explicitly defined number of instances. These are called Enumerations, because all the instances of the Type are known in advance and enumerated, and each instance must be one of these few possible values. The classic example of such a Type is Boolean, named after George Boole, which has exactly two instances: True and False. Another Enumeration would be the Days of the Week. Other Types can be simple but have an infinite number of possible instances. Examples of such Types are String for sequences of characters, and Positive Integer for the counting numbers. Other Types can be composed of simpler Types. For example, one way to represent an Integer would be to compose it from a Positive Integer and a Boolean, where the Boolean decides whether the Integer is positive or negative, and the Positive Integer represents the absolute value.

Not every Object has to be stored as a wiki page. For example, there is no need to store the number 2020 as an Object in the wiki, as it can be easily just created on the fly.

This is how Objects are built and represented. Objects of almost all Types are called Literals. A Literal is an Object that, when evaluated, results in itself. For example, when you evaluate the number 2020, the result is the number 2020. But there are two very special Types whose instances are not Literals, and these two types are References and Function Calls.

References are a special Type of Object that refers to a Persistent Object by its Z-ID. It basically just says “here, this Reference, should really be just this Object that is referenced to by this Z-ID”. Evaluating a Reference results in the referenced Object. A Reference does not need to be evaluated immediately, but can be evaluated whenever needed. In fact, it is sometimes impossible to evaluate all References fully, as it can easily lead to a recursion and infinite objects.

The other special Type of Object is the Function Call. A Function Call consists of a Function and a List of Arguments. Evaluating a Function Call is the core 'magic' of the whole system: it is basically replacing a Function Call with the result of that Function Call, e.g. evaluation would be replacing the Function Call to the Function with the label "length" and the argument "2020" of Type String with the value "4" of Type Positive Integer.

Function Calls are usually created on the fly. We wouldn’t, in general, create a new wiki page with a Persistent Object in which we store the Function Call described above, but rather we would send that Function Call to an evaluation engine which, in turn, evaluates the Function Call and returns the result. There is really not much more to the system than that. A Function Call is in many ways analogous to using a MediaWiki template with parameters.

I hope that this explanation made some sense and helped with understanding the planned system. We are currently developing the part of the system that allows contributors to create Types inside the wiki itself, so that the community can create and control which Types exist. Please feel free to ask questions.

The voting for the final round of the naming contest is ongoing. Voting will be open until Monday, November 16. If you haven’t already, please vote here and decide on a name for the new project where all of these Objects we described above will be available. The proposals we are voting on are, in reverse alphabetical order: Wikimedia Functions, Wikilambda, Wikifusion, Wikifunctions, Wikicodex, and Wikicode. Let us know your preferences and decide on the name of the new project by Monday!